Posterior simulation via the signed root log-likelihood ratio

Abstract

We explore the use of importance sampling based on signed root log-likelihood ratios for Bayesian computation. Approximations based on signed root log-likelihood ratios are used in two distinct ways; firstly, to define an importance function and, secondly, to define suitable control variates for variance reduction. These considerations give rise to alternative simulation-consistent schemes to MCMC for Bayesian computation in moderately parameterized regular problems. The schemes based on control variates can also be viewed as usefully supplementing computations based on asymptotic approximations by supplying external estimates of error. The methods are illustrated by a genetic linkage model and a censored regression model.